"p- Local block theory of
p- Solvable groups, Part II"
Abstract: Last week, using the Fong Correspondence, we defined the Kuelshammer-Puig twists associated with the centric objects of the fusion system of an arbitrary p-block. This week, we shall see how the Fong Correspondence appears again in the study of p-blocks of p-solvable groups. We shall also make use of the Glaubermann Correspondence,(which used to be a mysterious correspondence of characters until Puig explained it as a consequence of a fundamental property of endo-trivial-source modules). That will give us a technique for reducing to the case where the maximal normal p-regular subgroup is central, whereupon the Hall-Higman p-Constraint Theorem can be applied. We shall conclude, after Puig, that the fusion system of any p-block of a p-solvable group is the fusion system of a p-solvable group.
At the end, we shall comment briefly on adaptation of those classical methods to the study of multiplicity modules. We shall see why, to specify the multiplicity modules up to isomorphism, the Kuelshammer—Puig classes do not adequately specify the twisting; the central extensions need to be well-defined up to canonical isomorphism.
Date: Tuesday, 16 February 2016
Time: 13:40 - 15:30
Place: Mathematics Seminar Room, SA-141
All are cordially invited. Tea and biscuits after the seminar.